Orthogonal frequency division multiplexing (OFDM) transmitter and receiver windowing for adjacent channel interference (ACI) suppression and rejection

ABSTRACT

An optimum time domain windowing scheme for orthogonal frequency-division multiplexing (OFDM)-based waveforms in the sense of spectral concentration is proposed. Instead of evenly suppressing the sidelobes along the frequency, the sidelobe power is concentrated within a guard band while maximally suppressing the power for a desired frequency range. This is achieved by employing optimum finite duration pulses, prolate spheroidal wave functions (PSWF), to shape the OFDM transmit pulse. Also with per-subcarrier windowing scheme, the effect of inner subcarriers on sidelobes is diminished by utilizing the concentration bandwidth versus out-of-band power trade-off in PSWF and the multicarrier nature of the OFDM.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of and claims priority to currentlypending U.S. patent application Ser. No. 14/276,629, filed on May 13,2014, entitled “Orthogonal Frequency Division Multiplexing (OFDM)Transmitter And Receiver Windowing For Adjacent Channel Interference(ACI) Suppression And Rejection”, which claims priority to U.S.Provisional Patent Application No. 61/823,654, filed on May 15, 2013,entitled “Orthogonal Frequency Division Multiplexing (OFDM) TransmitterAnd Receiver Windowing For Adjacent Channel Interference (ACI)Suppression And Rejection”, the contents of which are incorporatedherein by reference in their entirety.

BACKGROUND OF THE INVENTION

Orthogonal frequency-division multiplexing (OFDM) signaling schemesdominate the existing and future wireless communication systems due tothe robustness of OFDM against multipath delay spread and theflexibility of OFDM in spectrum usage, making OFDM a strong candidatefor dynamic spectrum access (DSA)-based networks.

Despite the advantages of OFDM, an OFDM signal exhibits high spectralsidelobes as a result of the rectangular transmit pulse. An OrthogonalFrequency Division Multiplexing (OFDM) signal consists of sinusoidalsignals that are shaped with the rectangular function to generate therectangular transmit pulse. As a result of the shaping of the sinusoidalsignals utilizing a rectangular function, the OFDM signal suffers fromhigh out-of-band radiation due to high spectral sidelobes of sine shapedsubcarriers, resulting in adjacent channel interference (ACI).Additionally, the rectangular windowing used at the receiver results ina frequency response of the receiver filter (i.e. sine) having weak ACIrejection capability.

Two common countermeasures are known to reduce the out-of-band (OOB)radiation, the first is known as time domain windowing and the second isknown as frequency domain guard insertion. In time domain windowing, therectangular pulse is filtered by a windowing function that smooths thesymbol transitions. In frequency domain guard insertion, edge-bandsubcarriers are nulled to reduce spectral leakage to the out-of-band.

Additionally, there exist active techniques to suppress the spectralsidelobes. While these techniques give good suppression results, theyare primarily computationally complex due to the data-dependentoptimization problem and symbol-by-symbol processing. In addition, someof the techniques known in the art increase the peak-to-average powerratio (PAPR), degrade the bit error rate performance and require datadependent information for symbol recovery.

Alternatively, time domain windowing techniques with guard subcarrierinsertion are a much simpler and computationally efficient alternativeto reduce out-of-band radiation for OFDM based systems. In addition, theguarding effect of time domain windowing against multipath delay spreadis an inherent advantage of the windowing technique over theaforementioned scheme.

In accordance with the Uncertainty Principle, a signal cannot besimultaneously limited in time and frequency. As such, a rectangulartransmit pulse trades the spectral confinement in OFDM. With windowingtechniques, containment in the time domain is relaxed to achieve abetter spectrally-localized signal. However, conventional windowingschemes, e.g. commonly used raised cosine (RC) windowing, do not providethe optimum solution for time-frequency localization. In other words,the available frequency band near the main band of the signal, which canbe the guard band between the adjacent channels or the band between theedge subcarrier and the spectral mask to be complied, is not maximallyutilized with the conventional windowing techniques.

While other windowing functions may be utilized to reduce theout-of-band (OOB) power, these windowing functions do not optimallyaddress the need for the reduction and rejection of ACI.

Accordingly, what is needed in the art is an OFDM windowing techniquethat provides ACI suppression and rejection.

SUMMARY OF INVENTION

The present invention addresses the need for maximum ACI suppression atthe transmitter side through the implementation of a per-subcarriertransmit windowing technique which utilizes a unique windowing functionfor each individual subcarrier, or alternatively, a common windowingfunction applied to each individual subcarrier. At the receiver side,the present invention provides maximum ACI rejection through theimplementation of a per-subcarrier receiver windowing technique whichutilizes a unique windowing function for each individual subcarrier, oralternatively, a common windowing function applied to each individualsubcarrier

In accordance with the present invention, a method for time domainwindowing of a received Orthogonal Frequency Division Multiplexing(OFDM)-based signal is provided. The method includes, receiving anOFDM-based signal comprising a plurality of subcarriers and performingdiscrete prolate spheroidal windowing of each of the plurality ofsubcarriers of the received OFDM-based signal. The discrete prolatespheroidal windowing may be performed using a common windowing functionhaving a confinement band that is determined by the spectral location ofthe edge subcarrier to shape each of the plurality of subcarriers, as isthe case in even prolate windowing. Alternatively, the discrete prolatespheroidal windowing may be performed using a unique windowing functionfor each of the plurality of subcarriers, as is the case inper-subcarrier prolate windowing. The unique windowing function used toshape each of the plurality of subcarriers has a confinement band thatis determined by the summation of a guard band of the OFDM-based signaland the spectral distance between the subcarrier and the edgesubcarrier.

In accordance with the present invention, a method for time domainwindowing of an Orthogonal Frequency Division Multiplexing (OFDM)-basedsignal to be transmitted is provided. The method includes, performingdiscrete prolate spheroidal windowing of each of the plurality ofsubcarriers of the received OFDM-based signal and transmitting thesignal. The discrete prolate spheroidal windowing may be performed usinga common windowing function having a confinement band that is determinedby the spectral location of the edge subcarrier to shape each of theplurality of subcarriers, as is the case in even prolate windowing.Alternatively, the discrete prolate spheroidal windowing may beperformed using a unique windowing function for each of the plurality ofsubcarriers, as is the case in per-subcarrier prolate windowing. Theunique windowing function used to shape each of the plurality ofsubcarriers has a confinement band that is determined by the summationof a guard band of the OFDM-based signal and the spectral distancebetween the subcarrier and the edge subcarrier.

A system for performing the time domain windowing in accordance with thepresent invention may include a transceiver, or alternatively atransmitter and a receiver.

In accordance with the present invention, a time domain windowing schemethat provides the optimum confinement of the OFDM-based waveforms intime and a given frequency band is introduced. Optimum time-limitedfunctions in the sense of spectral containment, known as prolatespheroidal wave functions (PSWF), are adopted for maximum time-frequencylocalization that can be achieved with the transmitter waveform designin OFDM systems. By taking the mainlobe width vs. sidelobe suppressiontrade-off of PSWFs into account along with the multicarrier nature ofthe OFDM signals, the effect of inner subcarriers on sidelobes is nearlycanceled using a per-subcarrier windowing scheme. The proposed schemealso allows different suppression in lower and upper bands which can beutilized in cognitive radio (CR) applications.

Utilizing the filter-bank waveform design approach of the presentinvention, the significant advantages of OFDM, such as rectangularreceiver filtering with discrete Fourier transform (DFT) and one tapfrequency domain equalization with cyclic prefix (CP) usage aremaintained.

With the present invention, at the transmitter side, the available guardband near the transmission band is maximally utilized and hence optimumsuppression beyond the guard band is achieved. In other words, adjacentchannel interference (ACI) in the OFDM system is maximally suppressed byutilizing unique per-subcarrier transmit-windowing in accordance withthe present invention.

Additionally, at the receiver side, receiver windowing is also used forACI rejection. By utilizing a unique, optimum windowing function foreach received subcarrier, contribution from the transmission band of theadjacent channel is maximally reduced. In other words, in accordancewith the present invention, the guard band between the adjacent channelsis exploited while rejecting the ACI.

In an alternative embodiment, a common windowing function can beutilized for all subcarriers, instead of a unique windowing function foreach individual subcarrier. The common windowing function has alocalization range that is determined by only the guard band between theadjacent channels. Although this embodiment may result in a suboptimalsolution, it might have slightly simpler implementation since only onecommon windowing function is utilized for each of the subcarriers.

In contrast with the conventional techniques, such as raised cosine (RC)windowing, the proposed time domain windowing scheme provides moreflexibility, including asymmetric spectral shaping for lower and upperfrequencies and arbitrary guard band utilization without changing timingparameters of the transmitted signal, as well as superior spectralsuppression in the desired range.

BRIEF DESCRIPTION OF THE DRAWINGS

For a fuller understanding of the invention, reference should be made tothe following detailed description, taken in connection with theaccompanying drawings, in which:

FIG. 1(a) is a graph illustrating even windowing of an OFDM signalutilizing a common windowing function for each subcarrier, accordancewith the present invention.

FIG. 1(b) is a graph illustrating per-subcarrier prolate-windowing of anOFDM signal utilizing a unique windowing function for each subcarrier,in accordance with an embodiment of the present invention.

FIG. 2 is a graph illustrating the normalized power spectra comparisonsof other windowing solutions and the windowing solution in accordancewith an embodiment of the present invention.

FIG. 3 is a graph illustrating the normalized power spectra for evenprolate-windowing in accordance with an embodiment of the presentinvention.

FIG. 4 is a graph illustrating the ACLR performance of each windowingtype as a function of guard band size.

FIG. 5 is a table illustrating the spectral efficiency increase relativeto RC windowing for fixed channel bandwidth.

FIG. 6 is a block diagram illustrating an OFDM transmitter and an OFDMreceiver in accordance with an embodiment of the present invention.

FIG. 7 is a diagram illustrating a wireless network in accordance withan embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

A discrete time domain OFDM symbol with N subcarriers is generated byperforming inverse discrete Fourier transform (IDFT) to the complexbaseband data vector [X₀ ^((m)), X₁ ^((m)), . . . , X_(N−1) ^((m))]^(T),where m is the symbol index. Before defining the time domain symbol, DFTmatrix is denoted by F_(N,N) with entries

$\begin{matrix}{{( F_{N,N} )_{n,K} = {\mathbb{e}}^{{- j}\frac{2\pi}{N}{n{({k - {N/2}})}}}},n,{k = 0},\ldots\mspace{20mu},{N - 1.}} & (1)\end{matrix}$

The vector that represents mth time domain OFDM symbol is written as

$\begin{matrix}{{x^{(m)} = {\frac{1}{N}F_{N,N}^{*}X^{(m)}}},} & (2)\end{matrix}$

Where F_(N,N)* is complex conjugate of F_(N,N), i.e. IDFT matrix. Forthe time domain windowing implementation, a window matrix D_(N+G+2M,N)is defined whose column is the window function for correspondingsubcarrier including time extension of G-sample CP (cyclic prefix),M-samples pre-windowing, and M-samples post-windowing durations. Thus,elements of the window matrix can be written as(D _(N+G+2M,N))_(n,k) =w _(k)(n)  (3)

where w_(k)(n) is the window function, i.e. transmit pulse, for kthsubcarrier. Considering the overlapping of the consecutive symbols inthe windowing interval, windowed OFDM symbol to be transmitted, y^((m)),is written as

$\begin{matrix}{{y^{(m)} = {\frac{1}{N}\begin{bmatrix}{{( {{??}_{B} \circ \mathcal{F}_{B}^{*}} )X^{(m)}} + {( {{??}_{A} \circ \mathcal{F}_{A}^{*}} )X^{({m - 1})}}} \\{\mathcal{F}_{G}^{*}X^{(m)}} \\{F_{N,N}^{*}X^{(m)}}\end{bmatrix}}},} & (4)\end{matrix}$

where ∘ is Hadamard product operation,

_(B) and

_(A) are the subsets of D_(N+G+2M,N) containing only the rows thatcorrespond to pre-window (rows 0 to M−1) and post-window (rowsN+G+2M−1), respectively. Similarly.

_(B)*,

_(A)* and

_(G)* are the subsets of the F_(N,N)* with the rows regarding to thepre-window (rows N−G−M to N−G−1), the post window (rows 0 to M−1), andthe CP (rows N−G to N−1), respectively. Note that the entrywise productof the window matrix corresponding to the CP and useful symbol durationsare omitted in (4) since corresponding elements of the window matrixconsist of ones.

In the present invention, the window function, w(n), is obtained byfiltering the rectangular pulse with the windowing function, v(n), whichcorresponds to multiplying the sinc-shaped subcarrier spectrum by theFourier transform (FT) of v(n). Since the envelope of the subcarrierspectrum, before filtering, is monotonically decreasing along thefrequency, designing the v(n) for optimal spectral concentrationsatisfies the same objective for w(n).

The spectral concentration problem for finite duration pulses fallsunder the PSWF family, which relates to maximum concentration in timefor a band-limited signal, or maximum spectral concentration for atime-limited signal. When considering a digital baseband implementation,the discrete case of the windowing design is adopted. For the sequencev(n) that is index-limited from 0 to M−1, the ratio of the signal energyin the frequency range |f|≦W<1/2 to the total energy can be expressed as

$\begin{matrix}{{\lambda( {M,W} )} = \frac{\int_{- W}^{W}{{{V(f)}}^{2}\ {\mathbb{d}f}}}{\int_{{- 1}/2}^{1/2}{{{V(f)}}^{2}\ {\mathbb{d}f}}}} & (5)\end{matrix}$

where V(f) is the FT of v(n). By using Parseval's theorem, (5) can berewritten in terms of v(n) as

$\begin{matrix}{{\lambda( {M,W} )} = \frac{\sum\limits_{i = 0}^{M - 1}{\sum\limits_{n = 0}^{M - 1}{\frac{{v^{*}(n)}( {\sin( {2{{\pi W}( {l - n} )}} )} )}{\pi( {l - n} )}{v(l)}}}}{\sum\limits_{n = 0}^{M - 1}{{v(n)}}^{2}}} & (6)\end{matrix}$

It can be shown that the vector v(M, W)=[v(0), v(1), . . . , v(M−1)]^(T)that maximizes λ(M, W) must satisfyA(M,W)v(M,W)=λ(M,W)v(M,W)  (7)

where A(M, W) is an M×M matrix with entries (A(M, W))_(n,l)

${( {A( {M,W} )} )_{n,i} = \frac{\sin( {2\pi\;{W( {l - n} )}} )}{\pi( {l - n} )}},$n,l=0, . . . , M−1. Since the matrix is self-adjoint, the system in (7)has M distinct, real eigenvalues (concentration ratios) andcorresponding real eigenvectors (windowing sequences), which are alsoknown as discrete prolate spheroidal sequences (DPSS). Therefore, thespectral concentration problem for windowing functions reduces tofinding the eigenvector of A(M, W) that corresponds to the largesteigenvalue λ(M, W). Resulting in M-sample sequences that maximizes thesignal energy on the frequency interval [−W, W] is denoted as v_(PS)(M,W; n).

Guard bands are used to enable the signal spectrum to fall below adesired power level at adjacent channel frequencies. With prolatewindowing, this available buffer spectral zone is utilized to achievemaximum suppression beyond this guard band. In prevalent OFDM systems,the windowing operation is performed after obtaining the time domainOFDM symbol, i.e. one window function is used for every subcarrier. Whenthe same procedure is followed, the method of even prolate-windowingusing a common windowing function for each of the subcarriers, as taughtby the present invention, can be represented by defining the windowfunction as

$\begin{matrix}{{w_{k}(n)} = {{v_{PS}( {{M + 1},{\frac{\Gamma}{N};n}} )}*{{rect}( {n/( {N + G + M} )} )}}} & (8)\end{matrix}$

where Γ is the guard band that is normalized to subcarrier spacing whileN corresponds the normalized sampling frequency, so that the ratio ofthe Γ/N denotes the fractional bandwidth for optimum localization of thediscrete time OFDM signal. Note that the window sequence in (8) is not afunction of the subcarrier index, thus, the even prolate-windowingmethod inherits the conventional windowing implementation.

With reference to FIG. 1(a), the power spectra of the windowingfunctions for each subcarrier 100 and the combination of the windowingfunctions for the upper edge of the frequency band 105 are illustratedusing a common windowing function for each of the subcarriers, resultingin even prolate-windowing. As shown in FIG. 1(a) each subcarrier isshaped with a common windowing function whose confinement band isdetermined by the spectral location 110 of the edge subcarrier 115.

As the spectral concentration constraint of the prolate windowingfunctions is relaxed, superior suppression beyond the localization bandis achieved. By considering this trade-off, along with the multicarrierstructure of the OFDM waveform, the available guard band of individualsubcarriers, which have different distances to a fixed out of bandlocation, can be maximally exploited. Therefore, the windowing functionis designed per subcarrier such that the concentration ratio, W, foreach subcarrier is the summation of the guard band and the spectraldistance of the corresponding subcarrier to the edge subcarrier. Thewindow functions that constitutes D_(N+G+2M,N) in the per-subcarriercase can be written asw _(k)(n)=v _(PS)(M+1,W(k);n)*rect(n/(N+G+M))  (9)

where W(k) is the subcarrier-dependent optimization range. In order tomaximize utilization of the available band for each subcarrier,localization bandwidth is limited to lower guard-band, Γ_(U), that canbe represented as

$\begin{matrix}{{W(k)} = {\min( {\frac{k + \Gamma_{L}}{N},\frac{N - 1 - k + \Gamma_{U}}{N}} )}} & (10)\end{matrix}$

The per-subcarrier prolate windowing scheme, in accordance with thepresent invention, is depicted in FIG. 1(b). As shown in FIG. 1(b), thepower spectra of the windowing functions for each subcarrier 120 and thecombination of the windowing functions for the upper edge of thefrequency band 120 are illustrated using a unique windowing function foreach of the subcarriers, resulting in per-subcarrier prolate-windowing.FIG. 1(b) illustrates per-subcarrier prolate windowing employing aunique windowing function for each subcarrier wherein the optimizationrange of each subcarrier's windowing function is based on the subcarrierindex. By assigning relaxing concentration to their bands, the effect ofinner subcarriers is dramatically reduced. Confinement bandwidths 130,135, 140 are increased with the subcarrier spacing steps by keeping theoptimization range the same for whole signal spectrum. Reduced sidelobesof the windowing function of the inner subcarriers becomes negligiblecompared to the effect of the edge subcarrier 150, thus it can beconcluded that the spectral out-of-band emission is determined by onlythe edge subcarrier with per-subcarrier prolate windowing.

Also, in such scenarios that require different spectral suppression inlower and upper adjacent channels, as in emerging spectrum pooling andCR applications, asymmetric spectral suppression is possible by choosingthe lower guard band Γ_(L) and the upper guard band Γ_(U) independently.

Spectral suppression performance of any windowing type is a function ofthe amount of relaxation in the time domain, that is, longer windowingdurations provides better out-of-band suppression with the penalty ofreduced spectral efficiency. So far, the design of the OFDM waveformthat gives the optimum spectral localization for a given windowingduration M has been presented. However, to achieve the joint packing ofthe signal in time and frequency domains, different roll-off factorsneed to be investigated. Therefore, the problem becomes selecting thewindowing duration and the number of guard subcarriers to the givenspectral mask to be compiled. Therefore, the objective is to minimizethe total redundancy in the system, namely windowing duration, whilemaximizing the number of used subcarriers that maximizes the spectralefficiency by maximizing the information that is packed into the givenfrequency resource limited by the spectral mask.

In an exemplary embodiment, the performance of the windowing techniqueis presented having an OFDM system with N=256, G=16 and M=16. In thisexemplary embodiment, DC subcarrier is disabled. First, the out-of bandemissions are investigated for the optimization guard band ranges Γ=12,20 and 28 for unique per-subcarrier prolate windowing scheme. Thenormalized power spectra are shown in FIG. 2, including the conventionalOFDM system without symbol extension 200 and RC-windowed OFDM system 210for comparison. For each optimization range configuration. 215 (Γ=12),220 (Γ=20) and 225 (Γ=28), the per-subcarrier windowing scheme providesbetter suppression performance in the corresponding desired frequencyranges that are indicated by shaded areas, 230 (Γ=12), 235 (Γ=20) and240 (Γ=28). Additionally, even prolate-windowing using a commonwindowing function is considered a sub-optimal solution.

FIG. 3 illustrates the normalized power spectra for evenprolate-windowing 300 with Γ=30 together and with asymmetricalimplementation of the per-subcarrier case 305, 310 to point to theenhanced flexibility in spectral shaping. In the asymmetricalper-subcarrier implementation, optimization ranges are set as Γ_(L)=16305 and Γ_(U)=30 310, resulting in 20 dB additional suppression in theupper adjacent band 310 in comparison to the lower adjacent band 305.The power spectra for conventional OFDM windowing 320 and for RCwindowing 315 are also illustrated for comparison.

The effect of the present technique is further investigated on adjacentchannel leakage ratio (ACLR) as a function of guard band between thechannels. In FIG. 4, ACLR performances of each windowing type are givenas a function of guard band size. It is shown that the ACLR in evenprolate windowing 400 and per-subcarrier prolate windowing 405 inaccordance with the present invention, outperform the RC (raised-cosine)windowing 410 by around 5 dB up to the normalized guard band of 16 whichis also the windowing roll off factor, N/M. Beyond this range,suppression performance increases dramatically as the guard sizeincreases. Additionally, it is shown that the even prolate windowing 400and per-subcarrier prolate windowing 405 in accordance with the presentinvention, outperform the conventional windowing technique 415.

For a given spectral mask, i.e. frequency index, and the ACLR limit outof the index, even-prolate and per-subcarrier prolate windowing usageprovides better spectral efficiency by allowing more subcarrierpopulation and/or less windowing size utilization. The table shown inFIG. 5 includes the achieved spectral efficiency increase attained usingeven prolate windowing and per-subcarrier prolate windowing, inaccordance with the present invention, compared to widely used RCwindowing for different ACLR limits with fixed total channel bandwidth.The increment in spectral efficiency increases as the sidelobesuppression requirement is forced further, which is the criticalchallenge in CR scenarios. The technique of the present invention can beutilized for enhancing sidelobe suppression with fixed N and M or forimproving the spectral efficiency by populating more subcarriers for agiven spectral mask of ACLR limit.

Frequency resource that is employed for signals that fall below thedesired power level, is maximally utilized with prolate windowing forOFDM-based signals. The per-subcarrier windowing scheme of the presentinvention achieves optimum spectral containment, hence minimumout-of-band radiation in OFDM systems with time domain windowing.

In accordance with the present invention, a transmit windowing schemefor OFDM that maximally suppresses the ACI by utilizing the availableguard band between the adjacent channels as well as the band betweeneach subcarrier and the edge subcarrier is proposed. Similarly, themaximum localized windowing functions are used for the receiverwindowing so that the ACI rejection capability of the receiver filter isenhanced at the spectral range that the adjacent channel signal existsby optimally utilizing the guard band between the adjacent channelbands.

As shown with reference to FIG. 6, the method of the present inventionmay be employed in an OFDM transmitter 600 and/or an OFDM receiver 610.As shown with reference to FIG. 6, the OFDM transmitter 600 includes amodulation module 615 configured to receive incoming data and togenerate an OFDM-based signal comprising a plurality of subcarriers. TheOFDM transmitter 600 further includes an Inverse Fast Fourier Transform(IFFT) module, operating as a transmitter filter 625 to filter thesubcarriers of the OFDM-based signal using the proposed windowing schemeto generate a filtered OFDM-based signal. The filtered OFDM-based signalis then provided to a digital-to-analog module 620 of the transmitterprior to transmission of the filtered OFDM-based signal over thechannel. In addition, the OFDM receiver 610 includes ananalog-to-digital module 630 configured to receive incoming OFDM-basedsignals comprising a plurality of subcarriers. The analog-to-digitalmodule 630 provides the digital representation of the OFDM-base signalsto a Fast Fourier Transform (FFT) module, operating as a receiver filter635 to filter the subcarriers of the OFDM-based signal using theproposed windowing scheme and to generate a filtered OFDM-based signal.The filtered OFDM-based signal is then provided to a demodulation module640 of the receiver prior to transmission of the demodulated data overthe channel. As such, the proposed windowing scheme utilizes theavailable spectral room while shaping the transmitted signal andreceiver windowing. Thus, maximum ACI suppression at the transmitter 600and maximum ACI rejection at the receiver is achieved. Since transmitand receive windowing works independently, they can be used together oreither one can be implemented in transmitter 600 or receiver 610.

In a particular embodiment, the system and method of the presentinvention may be utilized in a wireless network system 700 employingmobile devices 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 asillustrated with reference to FIG. 7.

It will be seen that the advantages set forth above, and those madeapparent from the foregoing description, are efficiently attained andsince certain changes may be made in the above construction withoutdeparting from the scope of the invention, it is intended that allmatters contained in the foregoing description or shown in theaccompanying drawings shall be interpreted as illustrative and not in alimiting sense.

It is also to be understood that the following claims are intended tocover all of the generic and specific features of the invention hereindescribed, and all statements of the scope of the invention which, as amatter of language, might be said to fall there between.

What is claimed is:
 1. A method for time domain windowing of anOrthogonal Frequency Division Multiplexing (OFDM)-based signal, themethod comprising: receiving, at a receiver, an OFDM-based signalcomprising a plurality of subcarriers; identifying a spectral locationof an edge subcarrier of the plurality of subcarriers; identifying aspectral distance between each of the plurality of subcarriers and theedge subcarrier; identifying a unique windowing function for each of theplurality of subcarriers, the unique windowing function for each of theplurality of subcarriers having a confinement band that is determined bythe summation of a guard band of the OFDM-based signal and the spectraldistance between the subcarrier and the edge subcarrier; and performing,at the receiver, discrete prolate spheroidal windowing of each of theplurality of subcarriers of the received OFDM-based signal bymultiplying each of the plurality of subcarriers by the unique windowingfunction in the time domain to generate a filtered OFDM-based signal. 2.The method of claim 1, wherein performing, at the receiver, discreteprolate spheroidal windowing of each of the plurality of subcarriers ofthe received OFDM-based signal by multiplying each of the plurality ofsubcarriers by the unique windowing function in the time domain togenerate a filtered OFDM-based signal further comprises, multiplying asinc-shaped subcarrier spectrum of each of the plurality of subcarriersby the Fourier transform of the unique windowing function.
 3. The methodof claim 1, wherein identifying a unique windowing function for each ofthe plurality of subcarriers, the unique windowing function for each ofthe plurality of subcarriers having a confinement band that isdetermined by the summation of a guard band of the OFDM-based signal andthe spectral distance between the subcarrier and the edge subcarrier,further comprises: identifying a unique windowing function for an upperadjacent band of the ODFM-based signal based upon an upper guard bandand identifying a unique windowing function for a lower adjacent band ofthe OFDM-based signal based upon a lower guard band.
 4. A method fortime domain windowing of an Orthogonal Frequency Division Multiplexing(OFDM)-based signal, the method comprising: receiving, at a transmitter,an OFDM-based signal comprising a plurality of subcarriers; identifyinga spectral location of an edge subcarrier of the plurality ofsubcarriers; identifying a spectral distance between each of theplurality of subcarriers and the edge subcarrier; identifying a uniquewindowing function for each of the plurality of subcarriers, the uniquewindowing function for each of the plurality of subcarriers having aconfinement band that is determined by the summation of a guard band ofthe OFDM-based signal and the spectral distance between the subcarrierand the edge subcarrier; and performing, at the transmitter, discreteprolate spheroidal windowing of each of the plurality of subcarriers ofthe received OFDM-based signal by multiplying each of the plurality ofsubcarriers by the unique windowing function in the time domain togenerate a filtered OFDM-based signal; and transmitting, from thetransmitter, the filtered OFDM-based signal.
 5. The method of claim 4,wherein performing, at the transmitter, discrete prolate spheroidalwindowing of each of the plurality of subcarriers of the receivedOFDM-based signal further comprises, multiplying a sinc-shapedsubcarrier spectrum of each of the plurality of subcarriers by theFourier transform of the unique windowing function.
 6. The method ofclaim 4, wherein identifying a unique windowing function for each of theplurality of subcarriers, the unique windowing function for each of theplurality of subcarriers having a confinement band that is determined bythe summation of a guard band of the OFDM-based signal and the spectraldistance between the subcarrier and the edge subcarrier, furthercomprises: identifying a unique windowing function for an upper adjacentband of the ODFM-based signal based upon an upper guard band andidentifying a unique windowing function for a lower adjacent band of theOFDM-based signal based upon a lower guard band.
 7. A receiver for timedomain windowing of an Orthogonal Frequency Division Multiplexing(OFDM)-based signal, the receiver comprising: an analog to digitalmodule configured for receiving an OFDM-based signal comprising aplurality of subcarriers; a receiver filter coupled to the analog todigital module, the receiver filter configured for identifying aspectral location of an edge subcarrier of the plurality of subcarriers,for identifying a spectral distance between each of the plurality ofsubcarriers and the edge subcarrier, for identifying a unique windowingfunction for each of the plurality of subcarriers, the unique windowingfunction having a confinement band that is determined by the summationof the guard band of the OFDM-based signal and the spectral distancebetween the subcarrier and the edge subcarrier and for performingdiscrete prolate spheroidal windowing of each of the plurality ofsubcarriers of the received OFDM-based signal by multiplying each of theplurality of subcarriers by the unique windowing function in the timedomain to generate a filtered OFDM-based signal; and a demodulationmodule coupled to the receiver filter, the demodulation moduleconfigured for receiving the filtered OFDM-based signal and fordemodulating each of the plurality of subcarriers of the filteredOFDM-based signal.
 8. The system of claim 7, wherein the receiver filteris further configured for multiplying a sinc-shaped subcarrier spectrumof each of the plurality of subcarriers by the Fourier transform of theunique windowing function.
 9. The system of claim 7, wherein thereceiver filter is further configured for identifying a unique windowingfunction for an upper adjacent band of the ODFM-based signal based uponan upper guard band and identifying a unique windowing function for alower adjacent band of the OFDM-based signal based upon a lower guardband.
 10. A transmitter for time domain windowing of an OrthogonalFrequency Division Multiplexing (OFDM)-based signal, the transmittercomprising: a modulation module configured to receive a digital signalto be transmitted and configured to modulate the digital signal togenerate an OFDM-based signal comprising a plurality of subcarriers; atransmitter filter coupled to the modulation module, the transmitterfilter configured for identifying a spectral location of an edgesubcarrier of the plurality of subcarriers, for identifying a spectraldistance between each of the plurality of subcarriers and the edgesubcarrier, for identifying a unique windowing function for each of theplurality of subcarriers, the unique windowing function having aconfinement band that is determined by the summation of the guard bandof the OFDM-based signal and the spectral distance between thesubcarrier and the edge subcarrier and for performing discrete prolatespheroidal windowing of each of the plurality of subcarriers of thereceived OFDM-based signal by multiplying each of the plurality ofsubcarriers by the unique windowing function in the time domain togenerate a filtered OFDM-based signal; and a digital to analog modulecoupled to the transmitter filter, the digital to analog moduleconfigured for transmitting the filtered OFDM-based signal.
 11. Thesystem of claim 10, wherein the transmitter filter is further configuredfor multiplying a sinc-shaped subcarrier spectrum of each of theplurality of subcarriers by the Fourier transform of the uniquewindowing function.
 12. The system of claim 10, wherein the transmitterfilter is further configured for identifying a unique windowing functionfor an upper adjacent band of the ODFM-based signal based upon an upperguard band and identifying a unique windowing function for a loweradjacent band of the OFDM-based signal based upon a lower guard band.